If sin(Θ)=-5/8 and 180° < θ < 270°, what is the value of cos(θ)?
−sqrt39/64
-sqrt39/8 **my answer
sqrt39/64
sqrt39/8
correct
To find the value of cos(θ), we can use the Pythagorean identity: sin^2(θ) + cos^2(θ) = 1.
Given that sin(θ) = -5/8, we can calculate sin^2(θ) as follows:
sin^2(θ) = (-5/8)^2 = 25/64.
Now we can rearrange the formula to solve for cos^2(θ):
cos^2(θ) = 1 - sin^2(θ)
cos^2(θ) = 1 - 25/64
cos^2(θ) = 64/64 - 25/64
cos^2(θ) = 39/64
Since 180° < θ < 270°, we know that cosine is negative in that quadrant. Therefore, cos(θ) is -sqrt(39/64).
So, the correct answer is -sqrt(39/64), which is option -sqrt39/8.